siny*(x+siny)*dx+2x^2*cosY*dy=0

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Solution for siny*(x+siny)*dx+2x^2*cosY*dy=0 equation: 


Simplifying
siny(x + siny) * dx + 2x2 * cosY * dy = 0

Reorder the terms:
insy(insy + x) * dx + 2x2 * cosY * dy = 0

Reorder the terms for easier multiplication:
insy * dx(insy + x) + 2x2 * cosY * dy = 0

Multiply insy * dx
dinsxy(insy + x) + 2x2 * cosY * dy = 0
(insy * dinsxy + x * dinsxy) + 2x2 * cosY * dy = 0

Reorder the terms:
(dinsx2y + di2n2s2xy2) + 2x2 * cosY * dy = 0
(dinsx2y + di2n2s2xy2) + 2x2 * cosY * dy = 0

Multiply x2 * cosY
dinsx2y + di2n2s2xy2 + 2cosx2Y * dy = 0

Multiply cosx2Y * dy
dinsx2y + di2n2s2xy2 + 2cdosx2yY = 0

Reorder the terms:
2cdosx2yY + dinsx2y + di2n2s2xy2 = 0

Solving
2cdosx2yY + dinsx2y + di2n2s2xy2 = 0

Solving for variable 'c'.

Move all terms containing c to the left, all other terms to the right.

Add '-1dinsx2y' to each side of the equation.
2cdosx2yY + dinsx2y + -1dinsx2y + di2n2s2xy2 = 0 + -1dinsx2y

Combine like terms: dinsx2y + -1dinsx2y = 0
2cdosx2yY + 0 + di2n2s2xy2 = 0 + -1dinsx2y
2cdosx2yY + di2n2s2xy2 = 0 + -1dinsx2y
Remove the zero:
2cdosx2yY + di2n2s2xy2 = -1dinsx2y

Add '-1di2n2s2xy2' to each side of the equation.
2cdosx2yY + di2n2s2xy2 + -1di2n2s2xy2 = -1dinsx2y + -1di2n2s2xy2

Combine like terms: di2n2s2xy2 + -1di2n2s2xy2 = 0
2cdosx2yY + 0 = -1dinsx2y + -1di2n2s2xy2
2cdosx2yY = -1dinsx2y + -1di2n2s2xy2

Divide each side by '2dosx2yY'.
c = -0.5ino-1Y-1 + -0.5i2n2o-1sx-1yY-1

Simplifying
c = -0.5ino-1Y-1 + -0.5i2n2o-1sx-1yY-1

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